
where \(V_t\) , \(\alpha _t\) , \(q_t\)  and \(\theta _t\)  are air speed (ft/s), angle of attack (rad), pitch rate (rad/s) and pitch angle (rad), respectively. Moreover, \(T_{x,y}\)  (lbs), \(T_{z,t}\)  (lbs), \(T_{m,t}\)  (lbs–ft), \(D_t\)  (lbs), \(L_t\)  (lbs) and \(M_t\)  (lbs) denote the projection of the total engine thrust along the body's  \(X\) -axis, the projection of the total engine thrust along the body's  \(Z\) -axis, the pitching moment due to both engines, the drag force, the lift force and the aerodynamic pitching moment, respectively, with their nominal values given in [1]}. Defining \(x_t \triangleq [V_t \ \alpha _t \ q_t \ \theta _t]^\top \)  with \({x}_0\in [147,158] \times [0.04,0.05] \times [0.1,0.2] \times [0.04,0.05]\) , Figure REF  depicts the reachable set approximations for \(x_{1,t}\)  and \(x_{2,t}\)  of the system (REF ). For this system , \(T^{f_d}_O\)  is not computable, since the stationary/critical points of the vector fields cannot be obtained  analytically,  and as shown in Figure REF , \(T^{f_d}_R\)  obtains a tighter over-approximation than \(T^f_N,T^f_C\) , \(T^f_M\)  and \(T^{f_d}_L\) , with the best of \(T^f_N\) –\(T^{f_d}_R\)  showing further improvement.
